# name
Pairing of zeros and critical points for random polynomials

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Francesc Xavier Massaneda Clares

# metadata.dc.description.abstract[].value
[en] In this project we deal with random holomorphic polynomials $p_{N}$. Specifically, we study the relationship between zeros and critical points of $p_{N}$ considering two different probabilistic models. The first one is based on chosing independently and with uniform probability $N$ random points that will be the zeros of our polynomial $p_{N}$. The second model is that of the so-called parabolic Gaussian Analytic Function. In this second model, the distribution of points is more rigid, and the striking phenomenon continues to be observed: zeros and critical points appear, with high probability, in pairs.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Guillem de la Calle Vicente, 2021

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Pairing of zeros and critical points for random polynomials